I use a multi-niche site and I prefer it over landing pages. Here are my reasons:
1. SEO is easier.
2. Some reasonable amount of traffic that comes from one niche travels to other niches.
3. Plugins
4. You don't have to buy domain and hosting for every niche
5. Some WP themes have amazing presentation pages for the homepage.

I had 1 year exp with multi-niche site...I can say both of them convert the same..single niche LP looks more awesome, but multi niche sites are rising trust in the eye of the downloader(they think its something like cnet).Also multi niche sites must be HQ and with lot of content and categories.

One of the main reasons why you should go with a multi niche site. With the time you post more on your website and your domain authority increases. It'll be easier to rank.
Example:
I bought an EMD and after one week it's still nowhere. The niche which is published on my multi niche site with the same keyword is already page 2. And after a few weeks it'll be page 1.